Math Problem Statement

x^3(x + y) = y^2(4x − y) Find dy/dx by implicit differentiation

Solution

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Math Problem Analysis

Mathematical Concepts

Implicit Differentiation
Derivatives
Algebraic Manipulation

Formulas

Product rule: (uv)' = u'v + uv'
Implicit differentiation: differentiate both sides with respect to x and solve for dy/dx

Theorems

Product Rule
Chain Rule

Suitable Grade Level

Grades 11-12